This book studies the problems of stability and well-posedness, in the convex case. Stability means the basic parameters of a minimum problem do not vary much if we slightly change the initial data, while well-posedness means points with values close to the value of the problem must be close to actual solutions. In studying this, one is naturally led to consider perturbations of functions and of sets.
This book contains a condensed explication of hypertopologies and is intended to help those not familiar with hypertopologies learn how to use them in the context of optimization problems.
Rezensionen / Stimmen
From the reviews:
"In this book the author focuses on the study of convex functions and their properties under perturbations of data. In particular, he illustrates the ideas of stability and well-posedness and the connections between them. . This book is intended for graduate students and researchers especially in mathematics, physics and economics; to facilitate its use as a textbook, the author has included many exercises and examples of different levels of difficulty." (Davide La Torre, Mathematical Reviews, Issue 2006 h)
"This book studies convex functions in Banach spaces and the stable behavior under perturbations of the optimization problems associated to them. . An interesting feature of the book is the inclusion of some topics, like elements of game theory, hypertopologies and genericity of well-posedness, not usually found in textbooks devoted to convexity and optimization. . several useful examples, comments and remarks scattered throughout, and over 120 exercises of varying level difficulty. This book is suitable for graduate courses on convex optimization from a mathematical standpoint." (Tullio Zolezzi, Zentralblatt MATH, Vol. 1106 (8), 2007)
